Sampling from a multimodal distribution is a fundamental and challenging problem in computational science and statistics. Among various approaches proposed for this task, one popular method is Annealed Importance Sampling (AIS). In this paper, we propose an ensemble-based version of AIS by combining it with population-based Monte Carlo methods to improve its efficiency. By keeping track of an ensemble instead of a single particle along some continuation path between the starting distribution and the target distribution, we take advantage of the interaction within the ensemble to encourage the exploration of undiscovered modes. Specifically, our main idea is to utilize either the snooker algorithm or the genetic algorithm used in Evolutionary Monte Carlo. We discuss how the proposed algorithm can be implemented and derive a partial differential equation governing the evolution of the ensemble under the continuous time and mean-field limit. We also test the efficiency of the proposed algorithm on various continuous and discrete distributions.

翻译：从多峰分布中采样是计算科学与统计学中的一个基础性难题。针对该任务提出的各种方法中，退火重要性采样是一种常用算法。本文通过将退火重要性采样与基于种群的蒙特卡洛方法相结合，提出一种基于集成方法的改进版本，以提升其采样效率。通过在起始分布与目标分布之间的连续路径上跟踪一个集成系统而非单个粒子，我们利用集成内部的相互作用来促进对未发现模态的探索。具体而言，我们的核心思想是采用进化蒙特卡洛中使用的斯诺克算法或遗传算法。我们讨论了所提算法的实现方式，并推导了在连续时间与平均场极限下控制集成演化的偏微分方程。此外，我们在多种连续分布与离散分布上测试了所提算法的效率。